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Simplifying 68.5x + 80x2 = 173 Solving 68.5x + 80x2 = 173 Solving for variable 'x'. Reorder the terms: -173 + 68.5x + 80x2 = 173 + -173 Combine like terms: 173 + -173 = 0 -173 + 68.5x + 80x2 = 0 Begin completing the square. Divide all terms by 80 the coefficient of the squared term: Divide each side by '80'. -2.1625 + 0.85625x + x2 = 0 Move the constant term to the right: Add '2.1625' to each side of the equation. -2.1625 + 0.85625x + 2.1625 + x2 = 0 + 2.1625 Reorder the terms: -2.1625 + 2.1625 + 0.85625x + x2 = 0 + 2.1625 Combine like terms: -2.1625 + 2.1625 = 0.0000 0.0000 + 0.85625x + x2 = 0 + 2.1625 0.85625x + x2 = 0 + 2.1625 Combine like terms: 0 + 2.1625 = 2.1625 0.85625x + x2 = 2.1625 The x term is 0.85625x. Take half its coefficient (0.428125). Square it (0.1832910156) and add it to both sides. Add '0.1832910156' to each side of the equation. 0.85625x + 0.1832910156 + x2 = 2.1625 + 0.1832910156 Reorder the terms: 0.1832910156 + 0.85625x + x2 = 2.1625 + 0.1832910156 Combine like terms: 2.1625 + 0.1832910156 = 2.3457910156 0.1832910156 + 0.85625x + x2 = 2.3457910156 Factor a perfect square on the left side: (x + 0.428125)(x + 0.428125) = 2.3457910156 Calculate the square root of the right side: 1.531597537 Break this problem into two subproblems by setting (x + 0.428125) equal to 1.531597537 and -1.531597537.Subproblem 1
x + 0.428125 = 1.531597537 Simplifying x + 0.428125 = 1.531597537 Reorder the terms: 0.428125 + x = 1.531597537 Solving 0.428125 + x = 1.531597537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.428125' to each side of the equation. 0.428125 + -0.428125 + x = 1.531597537 + -0.428125 Combine like terms: 0.428125 + -0.428125 = 0.000000 0.000000 + x = 1.531597537 + -0.428125 x = 1.531597537 + -0.428125 Combine like terms: 1.531597537 + -0.428125 = 1.103472537 x = 1.103472537 Simplifying x = 1.103472537Subproblem 2
x + 0.428125 = -1.531597537 Simplifying x + 0.428125 = -1.531597537 Reorder the terms: 0.428125 + x = -1.531597537 Solving 0.428125 + x = -1.531597537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.428125' to each side of the equation. 0.428125 + -0.428125 + x = -1.531597537 + -0.428125 Combine like terms: 0.428125 + -0.428125 = 0.000000 0.000000 + x = -1.531597537 + -0.428125 x = -1.531597537 + -0.428125 Combine like terms: -1.531597537 + -0.428125 = -1.959722537 x = -1.959722537 Simplifying x = -1.959722537Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.103472537, -1.959722537}
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